Composition of Functions



Composition of Functions

Reflect (ABC over line m and label the image (A’B’C’. Then reflect (A’B’C’ over line n and label the image (A’’B’’C’’.

• Describe the relation between (ABC and (A’’B’’C’’.

• Draw [pic], [pic], and [pic]. What appears to be true about these lines?

• Measure AA’’, BB’’, and CC’’. What seems to be true?

• Measure the distance between lines m and n.

• How is the length AA’’ related to the distance between the parallel lines?

• How are [pic], [pic], and [pic] related to lines m and n?

• Can (A’’B’’C’’ be a reflection image of (ABC? Why or why not?

• What conjectures can you make about (ABC and (A’’B’’C’’? What properties of the figure are preserved under this composition of reflections?

• Can (A’’B’’C’’ be an image of (ABC using a single transformation? What transformation is that?

Reflect (ABC over line m and label the image (A’B’C’. Then reflect (A’B’C’ over line n and label the image (A’’B’’C’’.

• Describe the relation between (ABC and (A’’B’’C’’.

• Draw (APA’’ and (BPB’’. What appears to be true about these angles?

• Measure (APA’’ and (BPB’’. What seems to be true?

• How are these angles related to the angle formed by lines m and n?

• What properties of the figure are preserved under this composition of reflections?

• Can (A’’B’’C’’ be a reflection image of (ABC?

• Can (A’’B’’C’’ be a translation image of (ABC?

• What single transformation will make (A’’B’’C’’ the image of (ABC?

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[pic]

[pic]

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